When you interrupt people, you are telling them you are more interested in your take on what they are saying than what they are saying. Period. This is not encouraging.

If someone interrupts me, I assume they have no interest in the rest of the sentence and I just let them run away with the conversation. Usually it's really boring bc people who can't shut up also have no ability to edit down to the most important points, but why would I want to bore them by telling them things they are clearly not interested in the way they're boring me?